/export/starexec/sandbox2/solver/bin/starexec_run_C /export/starexec/sandbox2/benchmark/theBenchmark.c /export/starexec/sandbox2/output/output_files


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WORST_CASE(?,O(n^1))  

Preprocessing Cost Relations
=====================================

#### Computed strongly connected components 
0. recursive  : [eval_rank2_3/4,eval_rank2_4/5,eval_rank2_bb3_in/4,eval_rank2_bb4_in/4,eval_rank2_bb5_in/5]
1. recursive  : [eval_rank2__critedge_in/5,eval_rank2_bb1_in/3,eval_rank2_bb2_in/3,eval_rank2_bb3_in_loop_cont/6]
2. non_recursive  : [eval_rank2_stop/1]
3. non_recursive  : [eval_rank2_bb6_in/1]
4. non_recursive  : [eval_rank2_bb1_in_loop_cont/2]
5. non_recursive  : [eval_rank2_bb0_in/2]
6. non_recursive  : [eval_rank2_start/2]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_rank2_bb3_in/4
1. SCC is partially evaluated into eval_rank2_bb1_in/3
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is completely evaluated into other SCCs
5. SCC is partially evaluated into eval_rank2_bb0_in/2
6. SCC is partially evaluated into eval_rank2_start/2

Control-Flow Refinement of Cost Relations
=====================================

### Specialization of cost equations eval_rank2_bb3_in/4 
* CE 7 is refined into CE [8] 
* CE 5 is refined into CE [9] 
* CE 6 is refined into CE [10] 


### Cost equations --> "Loop" of eval_rank2_bb3_in/4 
* CEs [10] --> Loop 8 
* CEs [8] --> Loop 9 
* CEs [9] --> Loop 10 

### Ranking functions of CR eval_rank2_bb3_in(V_1,V_y_1,B,C) 
* RF of phase [8]: [-V_1+V_y_1+1,V_y_1]

#### Partial ranking functions of CR eval_rank2_bb3_in(V_1,V_y_1,B,C) 
* Partial RF of phase [8]:
  - RF of loop [8:1]:
    -V_1+V_y_1+1
    V_y_1


### Specialization of cost equations eval_rank2_bb1_in/3 
* CE 4 is refined into CE [11] 
* CE 3 is refined into CE [12,13,14,15] 


### Cost equations --> "Loop" of eval_rank2_bb1_in/3 
* CEs [15] --> Loop 11 
* CEs [13] --> Loop 12 
* CEs [14] --> Loop 13 
* CEs [12] --> Loop 14 
* CEs [11] --> Loop 15 

### Ranking functions of CR eval_rank2_bb1_in(V_x_0,V_y_0,B) 
* RF of phase [11,12,14]: [V_x_0/2-1/2]

#### Partial ranking functions of CR eval_rank2_bb1_in(V_x_0,V_y_0,B) 
* Partial RF of phase [11,12,14]:
  - RF of loop [11:1,12:1]:
    V_x_0/2-1/2
  - RF of loop [14:1]:
    V_x_0-1


### Specialization of cost equations eval_rank2_bb0_in/2 
* CE 2 is refined into CE [16,17] 


### Cost equations --> "Loop" of eval_rank2_bb0_in/2 
* CEs [17] --> Loop 16 
* CEs [16] --> Loop 17 

### Ranking functions of CR eval_rank2_bb0_in(V_m,B) 

#### Partial ranking functions of CR eval_rank2_bb0_in(V_m,B) 


### Specialization of cost equations eval_rank2_start/2 
* CE 1 is refined into CE [18,19] 


### Cost equations --> "Loop" of eval_rank2_start/2 
* CEs [19] --> Loop 18 
* CEs [18] --> Loop 19 

### Ranking functions of CR eval_rank2_start(V_m,B) 

#### Partial ranking functions of CR eval_rank2_start(V_m,B) 


Computing Bounds
=====================================

#### Cost of chains of eval_rank2_bb3_in(V_1,V_y_1,B,C):
* Chain [[8],10]: 1*it(8)+0
  Such that:it(8) =< V_y_1-C

  with precondition: [B=2,V_1>=1,C>=V_1,V_y_1>=C+1] 

* Chain [[8],9]: 1*it(8)+0
  Such that:it(8) =< V_y_1-C

  with precondition: [B=2,V_1=C+1,V_1>=1,V_y_1>=V_1] 

* Chain [10]: 0
  with precondition: [B=2,V_y_1=C,V_1>=1,V_y_1>=V_1] 

* Chain [9]: 0
  with precondition: [B=2,V_y_1=C,V_1>=1,V_1>=V_y_1+1] 


#### Cost of chains of eval_rank2_bb1_in(V_x_0,V_y_0,B):
* Chain [[11,12,14],15]: 2*it(11)+1*it(14)+2*s(5)+0
  Such that:it(14) =< V_x_0
aux(5) =< V_x_0/2
aux(6) =< V_x_0/2+V_y_0
it(11) =< aux(5)
it(14) =< aux(5)
s(5) =< aux(6)
it(14) =< aux(6)

  with precondition: [B=3,V_x_0>=2,V_y_0>=0] 

* Chain [15]: 0
  with precondition: [B=3,1>=V_x_0] 


#### Cost of chains of eval_rank2_bb0_in(V_m,B):
* Chain [17]: 0
  with precondition: [1>=V_m] 

* Chain [16]: 1*s(7)+2*s(10)+2*s(11)+0
  Such that:s(7) =< V_m
s(8) =< V_m/2
s(9) =< 3/2*V_m
s(10) =< s(8)
s(7) =< s(8)
s(11) =< s(9)
s(7) =< s(9)

  with precondition: [V_m>=2] 


#### Cost of chains of eval_rank2_start(V_m,B):
* Chain [19]: 0
  with precondition: [1>=V_m] 

* Chain [18]: 1*s(12)+2*s(15)+2*s(16)+0
  Such that:s(12) =< V_m
s(13) =< V_m/2
s(14) =< 3/2*V_m
s(15) =< s(13)
s(12) =< s(13)
s(16) =< s(14)
s(12) =< s(14)

  with precondition: [V_m>=2] 


Closed-form bounds of eval_rank2_start(V_m,B): 
-------------------------------------
* Chain [19] with precondition: [1>=V_m] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [18] with precondition: [V_m>=2] 
    - Upper bound: 5*V_m 
    - Complexity: n 

### Maximum cost of eval_rank2_start(V_m,B): nat(3/2*V_m)*2+nat(V_m)+nat(V_m/2)*2 
Asymptotic class: n 
* Total analysis performed in 158 ms.